Comparing universal covers in polynomial time

Fiala, J.; Paulusma, D.

Abstract

The universal cover T G of a connected graph G is the unique (possible infinite) tree covering G, i.e., that allows a locally bijective homomorphism from T G to G. Universal covers have major applications in the area of distributed computing. It is well-known that if a graph G covers a graph H then their universal covers are isomorphic, and that the latter can be tested in polynomial time by checking if G and H share the same degree refinement matrix. We extend this result to locally injective and locally surjective homomorphisms by following a very different approach. Using linear programming techniques we design two polynomial time algorithms that check if there exists a locally injective or a locally surjective homomorphism, respectively, from a universal cover T G to a universal cover T H . This way we obtain two heuristics for testing the corresponding locally constrained graph homomorphisms. As a consequence, we have obtained a new polynomial time algorithm for testing (subgraph) isomorphism between universal covers, and for checking if there exists a role assignment (locally surjective homomorphism) from a given tree to an arbitrary fixed graph H.

Citation

Fiala, J., & Paulusma, D. (2008, December). Comparing universal covers in polynomial time. Presented at 3rd International Computer Science Symposium in Russia, Moscow, Russia

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 3rd International Computer Science Symposium in Russia
• Publication Date: Jan 1, 2008
• Deposit Date: Oct 6, 2010
• Print ISSN: 0302-9743
• Publisher: Springer Verlag
• Pages: 158-167
• Series Title: Lecture notes in computer science
• Series Number: 5010
• Edition: 3rd
• Book Title: Computer science – theory and applications, Third International Computer Science Symposium in Russia, CSR 2008, 7-12 June 2008, Moscow, Russia ; proceedings.
• DOI: https://doi.org/10.1007/978-3-540-79709-8_18
• Public URL: https://durham-repository.worktribe.com/output/1159609